In 729 litres solution of acid and water, the ratio of acid and water is 7 : 2. How many litres of water must be added to it to get the solution in which the ratio of acid and water is 5 : 3?

178.2

Acid : Water = 7 : 2

⇒ (7 + 2)units = 729

⇒ 9 units = 729

⇒ 1 unit = 81L

⇒ Acid = 7 x 81 = 567 L

⇒ Water = 2 x 81 = 162 L

Let quantity of added water be a,

⇒ \(\frac{567}{162 + a}\) = \(\frac{5}{3}\)

⇒ 3 x 567 = 5 x 162 + 5x

⇒ 1701 = 810 + 5x

⇒ 5x = 1701 - 810

⇒ x = 178.2 L

Therefore, 178.2 L of water must be added to make the ratio of acid and water 5 : 3.